I used to believe as you do, that partial inductances are useful to obtain
some first-cut answers. Over the years, I've changed my mind. I believe
that the potential for misuse from partial inductances outweighs their
benefits, and I'm now doing all my signal integrity modeling with loop
inductances. I'm much happier. :-)

Here are some of the problems I see with partial inductances:

1.) They are arbitrary; as Brian Young points out in his wonderful new
book, you can add any constant you want to the partial inductance matrix
without changing the physical result. Different techniques for calculating
partial inductance give different answers --- witness the discussion we've
just had on this point.

2.) When you use partial inductances in SPICE simulations, they give you
things that look like "ground bounce": voltage differences across large
sections of your circuit, where it is impossible to make a unique physical
measurement of voltage because of linked flux. Brian Young again points out
that ground bounce is not unique; it depends on your definition of partial
inductance. You can be mislead by how chip ground is bouncing with respect
to module ground in your simulation --- it looks like something real, but
it's not. When you use loop inductances, and use SPICE node 0 to represent
local reference everywhere, you can't be mislead; there's no node voltage in
your simulation that looks like ground bounce.

3.) If you use partial inductances in your SPICE simulations, you have to
make sure that all the current in your simulation moves from one side of
your circuit to the other only through the partial inductances. If you have
node 0 on both sides, for example, you've violated the assumptions under
which partial inductance is valid. And it can be very hard to avoid node 0
sometimes, and it appears that having large sections of your circuit
isolated from node 0 makes convergence more difficult.

4.) Partial inductances are completely invalid without mutual inductances,
but there's a great tendency to ignore them as a "first-pass engineering
assumption". This is natural; all of engineering is about ignoring things.
:-) But it just doesn't work with partial inductances. At best, you're
making assumptions about where the return path is (and different ways of
calculating partial inductances make different assumptions); at worst, you
miss the entire point of the exercise. Without partial mutual inductances,
there's no reason to put power and ground planes close to each other.

Basically, my feeling now is that partial inductances are a wonderful tool
for calculating inductance in the standard signal integrity situation where
the full loop is not completely known (package without chip or board, for
example). But I think now they should remain a computational tool, and that
the models that are eventually generated should be based on loop
inductances.

I'm working on a paper explaining these points in more detail and talking
about how we've been using loop inductance rather than partial inductance
for package modeling here at Compaq. I hope to present the paper at EPEP'01
here in Massachusetts. I would appreciate any comments people might have.

Good point. Strictly speaking and from a closed solution (analytical)
point, we should not attach any physical significance to individual partial
inductances. But, from a discretized solution (computational) point - which
is the way we are being driven by technology, such as the finite-difference
time-domain for example, is it not a mathematical convenience to consider
those individual partial inductances - especially where one does not know
how and where the current loops are closing - to obtain some first-cut
answers? Just another view.

Regards,
Sainath

Mike Jenkins wrote:

All,

FWIW, I recall that the IBM Yorktown researchers who developed the
partial inductance concept included on the first page of the research
report the quote from Weber to the effect that inductance makes no
sense unless one considers the entire loop of current. I guess
they were sensitive to not inducing readers to attach any physical
significance to the individual partial inductances.

Regards,
Mike

"Tsuk, Michael" wrote:
>
> Doug McKean wrote:
>
> ------------------------------------------------------------
> Okay, well here goes ...
>
> It's easy to see that if a signal trace had a return trace as a
> wire (shown by a dotted line), the following would cause
> the creation of a loop.
>
> |
> |
> |
> +----------+
> . |
> return . | signal
> trace . Loop | trace
> . |
> +----------+
> |
> |
> |
>
> Obviously from this construction, the inductance of the
> return wire would be less than if the return wire was
> underneath and following the longer path of the signal
> trace. Thus, my questioning the path of less inductance
> rule.
>
> ------------------------------------------------------------
>
> The confusion comes from the fact that you've ignored mutual inductance
> here, which acts to reduce the total inductance of this circuit. The
return
> current will choose the path (or combination of paths) that minimize the
> *total* loop inductance, not the partial inductance of the return alone.
>
> In general, you can never ignore mutual inductance. :-( This is
> particularly true if you're dealing with partial inductances, which are
only
> useful if all mutuals are included.
>
> Even more interesting to my mind is the sign error you made in calculating

> the direction of the magnetic force on your currents. The magnetic force
> between two parallel currents draws them *together* if the currents are in

> the same direction, and pushes them *apart* if they are in opposite
> directions. Check any electromagnetics text. Your mistake is that you
> assumed a *positive* charge when you equated the current direction with
the
> velocity of your particle, but a *negative* charge when you calculated the

> force.
>
> Why the apparent effect of minimizing inductance works in the opposite
> direction is very interesting. I think I have the answer, but I'm not
sure.
> I'd appreciate any input people might have.
>
> --
> Michael Tsuk
> Compaq AlphaServer Product Development
> (508) 467-4621
>
> -----Original Message-----
> From: Doug McKean [ mailto:dmckean@corp.auspex.com
<mailto:dmckean@corp.auspex.com> ]
> Sent: Monday, March 19, 2001 4:08 PM
> To: si-list@silab.eng.sun.com
> Cc: Doug McKean
> Subject: Re: [SI-LIST] : Re: approximations for partial self inductance
> - WHY
>
> ------------------------------------------------------------
> Okay, well here goes ...
>
> It's easy to see that if a signal trace had a return trace as a
> wire (shown by a dotted line), the following would cause
> the creation of a loop.
>
> |
> |
> |
> +----------+
> . |
> return . | signal
> trace . Loop | trace
> . |
> +----------+
> |
> |
> |
>
> Obviously from this construction, the inductance of the
> return wire would be less than if the return wire was
> underneath and following the longer path of the signal
> trace. Thus, my questioning the path of less inductance
> rule.
>
> As shown above, the signal current path forms the bottom,
> right side, and top parts of a loop. The return current path
> forms the left side of the a loop.
>
> Assume the signal path is bound one-dimensionally by the
> confines of the trace. Assume the return path is bound two
> dimensionally by the confines of the ground plane. In other
> words, the signal path is not free to move at all, but the
> return path is free to move in 2-D (up, down, left, right
> in the above picture).
>
> Now, assume the return path in the ground IS as shown above
> with the signal path and the return path. We have a loop. The
> virtual current loop if you will, circulates causing a soloenoidal
> action creating a magnetic field in the center. As such, using
> the right hand rule for current vs. magnetic fields, we have a
> magnetic field coming out of the monitor. The magnetic field
> lines are normal to the screen of the monitor.
>
> Using the other right hand rule for charges moving in a magnetic
> field by way of the Lorentz force, my thumb points in the direction
> of current flow, my fingers point in the direction of the magnetic
> field, and my palm points in the direction that the a positive
> charge would be pushed. With a negative charge, the push is
> from the back of your hand or toward the signal wire. Since
> the return current is bound only by a plane, it seeks to be
> under the signal trace. And it would continue to balance
> itself there.
>
> Turn the path of the signal current around and the return
> current, everything reverses including the direction of the
> magnetic field, and we still have a Lorentz force pusing the
> return current back to the signal trace.
>
> A DC return current in the ground plane wouldn't cause such
> action. It would follow only the path of least resistance.
>
> This is lots more wordy than if I was face to face and showed
> with the right hand rule for negative charge in a magnetic field.
>
> Regards, Doug McKean
> ------------------------------------------------------------
>
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